电子课本网 第73页

第73页

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​$=\frac {1}{2}-\frac {1}{3}+\frac {1}{3}-\frac {1}{4}+···+\frac {1}{9}-\frac {1}{10}$​
​$=\frac {1}{2}-\frac {1}{10}$​
​$=\frac {2}{5}$​
​$=1-(\frac {1}{20}+\frac {1}{30}+\frac {1}{42}+\frac {1}{56}+\frac {1}{72}+\frac {1}{90}+\frac {1}{110}+\frac {1}{132})$​
​$=1-(\frac {1}{4}-\frac {1}{5}+\frac {1}{5}-\frac {1}{6}+···+\frac {1}{11}-\frac {1}{12})$​
​$=1- (\frac {1}{4}-\frac {1}{12})$​
​$=1-\frac {1}{6}$​
​$=\frac {5}{6}$​